1.
Triangle Theorem: In a
triangle, the hypotenuse is twice as long as the shorter leg and the longer leg is
times as long as the shorter leg.
a. The longer leg is the altitude, so by the theorem, the altitude is 5
b. Let x be the altitude, then by the Pythagorean Theorem we have
We only need the positive root since the altitude is a length.
2.
By the Pythagorean Theorem we have:
We only need the postive root since n, and c are lengths. The
formula means the length of the hypotenuse is 
times the length of the leg.
3.The measure of the shorter leg of a
triangle is s. The measure of the longer leg is s
and the measure of the hypotenuse is 2s.
4. If the measure of a leg of an isosceles triangle is l, then
the measure of the hypotenuse is l.
5. Find the length of the diagonal in the square below:
By the isosceles right triangle theorem, the diagonal, which
is the hypotenuse is times the length
of the side, so it is 1'', or ''.
